Selected quad for the lemma: end_n

Word A	Word B	Word C	Word D	Occurrence	Frequency Band	MI	MI Band	Prominent
end_n	east_n	point_n	west_n	1,970	5	9.4719	5	true

Text snippets containing the quad

ID	Title	Author	Corrected Date of Publication (TCP Date of Publication)	STC	Words	Pages
A93912	The description and use of the universall quadrat. By which is performed, with great expedition, the whole doctrine of triangles, both plain and sphericall, two severall wayes with ease and exactness. Also the resolution of such propositions as are most usefull in astronomie, navigation, and dialling. By which is also performed the proportioning of lines and superficies: the measuring of all manner of land, board, glasse; timber, stone. &c. / By Thomas Stirrup, Philomathemat.	Stirrup, Thomas.	1655 (1655)	Wing S5687; Thomason E823_8; ESTC R207671	96,908	228

i_o seek_v in_o the_o ecliptic_a and_o follow_v the_o parallel_n that_o pass_v thereby_o to_o the_o horizon_n i_o find_v it_o there_o to_o cut_v 19_o deg_fw-la 7_o min._n count_v from_o the_o centre_n and_o such_o be_v the_o amplitude_n require_v the_o sphere_n be_v set_v to_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n chap._n xxx_o have_v the_o latitude_n of_o the_o place_n with_o the_o declination_n of_o any_o star_n to_o find_v his_o amplitude_n first_o the_o sphere_n to_o the_o latitude_n be_v set_v if_o the_o star_n be_v therein_o place_v follow_v the_o parallel_n of_o declination_n whereon_o he_o stand_v to_o the_o horizon_n and_o if_o he_o be_v not_o in_o the_o instrument_n get_v his_o declination_n by_o the_o seven_o chap._n or_o otherwise_o by_o some_o table_n for_o that_o purpose_n which_o find_v seek_v it_o in_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n &_o follow_v the_o parallel_n thereof_o to_o the_o horizon_n and_o if_o it_o cut_v the_o horizon_n it_o there_o show_v the_o amplitude_n but_o if_o it_o cut_v it_o not_o then_o do_v not_o that_o star_n set_v or_o go_v down_o under_o our_o horizon_n as_o for_o example_n let_v it_o be_v require_v to_o find_v the_o amplitude_n of_o arcturus_n i_o look_v in_o my_o instrument_n for_o arcturus_n and_o i_o find_v he_o place_v upon_o the_o parallel_n of_o 21_o d._n 10_o min._n of_o north_n declination_n as_o it_o be_v just_a in_o the_o horizon_n at_o 36_o deg_fw-la 23_o min._n from_o the_o centre_n and_o such_o be_v his_o amplitude_n and_o if_o you_o will_v have_v the_o amplitude_n of_o the_o lion_n heart_n look_v in_o your_o instrument_n and_o you_o shall_v find_v he_o place_v upon_o the_o parallel_n of_o 13_o deg_fw-la 42_o min._n of_o north_n declination_n which_o if_o you_o follow_v to_o the_o horizon_n you_o shall_v find_v it_o there_o cut_v 22_o deg_fw-la 54_o min._n and_o such_o be_v the_o amplitude_n of_o the_o lion_n heart_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n but_o if_o you_o will_v seek_v the_o amplitude_n of_o the_o bright_a star_n call_v the_o harp_n you_o shall_v find_v he_o place_v upon_o the_o parallel_n of_o 38_o deg_fw-la 30_o min._n north_n declination_n but_o this_o parallel_n cut_v not_o the_o horizon_n therefore_o he_o go_v not_o under_o our_o horizon_n at_o all_o in_o the_o aforesaid_a latitude_n of_o 52_o deg_fw-la 30_o min._n but_o when_o he_o be_v in_o his_o low_a direct_o in_o the_o north_n he_o be_v just_a one_o degree_n of_o height_n chap._n xxxii_o have_v the_o declination_n and_o amplitude_n of_o the_o sun_n to_o find_v the_o latitude_n of_o the_o place_n count_n the_o declination_n upon_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n and_o the_o amplitude_n upon_o the_o horizon_n from_o the_o centre_n the_o same_o way_n with_o the_o declination_n then_o move_v the_o sphere_n to_o and_o fro_o until_o the_o amplitude_n and_o the_o parallel_n of_o declination_n meet_v both_o in_o one_o point_n the_o south_n end_n of_o the_o horizon_n shall_v cut_v the_o meridian_n at_o the_o compliment_n of_o the_o latitude_n require_v as_o for_o example_n let_v the_o sun_n declination_n be_v 11_o deg_fw-la 30_o min._n and_o his_o amplitude_n 19_o deg_fw-la 7_o min._n if_o you_o move_v the_o sphere_n until_o the_o 19_o deg_fw-la 7_o min._n one_o the_o horizon_n fall_v direct_o on_o the_o parallel_n of_o 11_o deg_fw-la 30_o min._n the_o south_n end_n of_o the_o horizon_n will_v cut_v the_o limb_n at_o 37_o deg_fw-la 30._o min._n and_o such_o be_v the_o height_n of_o the_o equinoctial_a which_o be_v take_v out_o of_o 90_o deg_fw-la leave_v 52_o deg_fw-la 30_o min._n for_o the_o latitude_n of_o the_o place_n which_o be_v require_v chap._n xxxii_o the_o latitude_n of_o the_o place_n and_o the_o amplitude_n of_o the_o sun_n be_v give_v to_o find_v his_o declination_n first_o set_v the_o sphere_n to_o the_o latitude_n propose_v then_o count_v the_o amplitude_n upon_o the_o horizon_n and_o where_o it_o shall_v end_v shall_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree-line_n will_v there_o show_v you_o the_o declination_n require_v as_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o amplitude_n be_v 19_o deg_fw-la 7_o min._n if_o you_o first_o place_n the_o sphere_n to_o the_o latitude_n and_o then_o count_v 19_o deg_fw-la 7_o min._n upon_o the_o horizon_n there_o shall_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree_n line_n shall_v there_o give_v you_o 11_o deg_fw-la 30_o min._n the_o declination_n require_v chap._n xxxiii_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v his_o height_n in_o the_o vertical_a circle_n first_o set_v the_o sphere_n to_o the_o latitude_n give_v then_o count_v the_o declination_n give_v among_o the_o almicanter_n from_o both_o end_n of_o the_o horizon_n towards_o the_o zenith_n and_o thereto_o place_v the_o thread_n parallel_v to_o the_o horizon_n and_o where_o the_o thread_n so_o place_v cut_v the_o axletree-line_n or_o six_o a_o clock_n hour-line_n there_o be_v the_o altitude_n require_v as_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n if_o you_o count_v this_o 11._o deg_fw-la 30_o min._n from_o both_o end_n of_o the_o horizon_n among_o the_o almicanter_n and_o place_v the_o thread_n thereto_o it_o shall_v lie_v parallel_n to_o the_o horizon_n and_o cut_v the_o axle-tree-line_n at_o 14_o deg_fw-la 33_o min._n and_o such_o be_v the_o sun_n height_n when_o he_o be_v direct_o in_o the_o east_n or_o west_n point_v which_o be_v require_v or_o if_o you_o place_v the_o horizon_n to_o 52_o deg_fw-la 30_o min._n in_o the_o limb_n count_v from_o the_o equator_fw-la and_o count_v the_o declination_n upon_o the_o axletree-line_n viz._n 11_o deg_fw-la 30_o min._n the_o parallel_n thereof_o shall_v cut_v the_o horizon_n at_o 14_o deg_fw-la 33_o min._n for_o the_o height_n of_o the_o sun_n in_o the_o vertical_a circle_n the_o same_o as_o before_o chap._n xxxiv_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v the_o time_n of_o his_o come_n to_o the_o east_n or_o west_n point_n first_o set_v the_o planisphere_n to_o the_o latitude_n give_v then_o place_v the_o thread_n upon_o the_o zenith_n and_o the_o nadir_n so_o shall_v it_o cut_v the_o horizon_n at_o right_a angle_n in_o the_o centre_n and_o the_o parallel_n of_o declination_n at_o the_o time_n from_o six_o count_v among_o the_o meridian_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o deg_fw-la 30_o min._n and_o the_o sun_n declination_n 11_o deg_fw-la 30_o min._n first_o place_z the_o horizon_n to_o 37_o deg_fw-la 30_o min._n the_o compliment_n of_o the_o latitude_n below_o the_o south_n end_n of_o the_o equator_fw-la then_o place_v the_o thread_n to_o the_o zenith_n and_o nadir_n that_o be_v to_o 52_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o equator_fw-la and_o as_o much_o below_o the_o north_n end_v thereof_o the_o thread_n be_v fix_v shall_v cut_v the_o horizon_n at_o right_a angle_n in_o the_o centre_n and_o also_o the_o parallel_n of_o 11_o deg_fw-la 30_o min_fw-mi at_o the_o meridian_n of_o 9_o deg_fw-la or_o in_o time_n at_o 36_o minute_n from_o the_o hour_n of_o six_o and_o such_o be_v the_o distance_n of_o time_n betwixt_o the_o hour_n of_o six_o and_o the_o sun_n come_v to_o the_o east_n or_o west_n point_n which_o be_v require_v chap._n xxxv_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v his_o height_n at_o the_o hour_n of_o six_o first_o set_v the_o horizon_n to_o the_o compliment_n of_o the_o latititude_n below_o the_o south_n end_n of_o the_o equator_fw-la or_o the_o equator_fw-la to_o the_o compliment_n of_o the_o latitude_n above_o the_o south_n end_n of_o the_o horizon_n which_o be_v all_o one_o then_o seek_v the_o declination_n upon_o the_o axletree-line_n and_o place_v the_o thread_n thereunto_o parallel_v to_o the_o horizon_n by_o help_n of_o the_o almicanter_n at_o both_o end_n thereof_o so_o shall_v the_o thread_n show_v among_o those_o almicanter_n the_o height_n of_o the_o sun_n require_v thus_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o sun_n declination_n be_v 11_o deg_fw-la 30_o min._n i_o first_o set_v the_o equator_fw-la 37_o deg_fw-la 30_o min._n above_o the_o horizon_n and_o then_o place_v the_o thread_n to_o 11_o deg_fw-la 30_o min._n count_v in_o the_o axletree-line_n and_o move_v the_o end_n thereof_o to_o and_o fro_o until_o the_o thread_n lie_v parallel_n to_o the_o horizon_n which_o will_v be_v when_o both_o end_n of_o the_o thread_n cut_v like_o degree_n from_o the_o horizon_n upon_o

the_o ascensional_a difference_n 1_o hour_n 1_o minute_n add_v to_o 6_o hour_n make_v 7_o hour_n 1_o minute_n the_o semidiurnal_a arch_n or_o the_o time_n of_o sun_n set_v which_o be_v double_v give_v 14_o hour_n 2_o minute_n for_o the_o diurnal_a arch_n this_o be_v take_v out_o of_o 24_o hour_n leave_v 9_o hour_n 58_o minute_n for_o the_o nocturnal_a arch_n the_o half_a of_o which_o 9_o hour_n 58_o minute_n be_v 4_o hour_n 59_o minute_n the_o time_n of_o sun_n rise_v or_o 7_o hour_n 1_o minute_n take_v out_o of_o 12_o hour_n leave_v 4_o hour_n 59_o minute_n the_o time_n of_o sun_n rise_v but_o if_o the_o declination_n be_v southwards_o then_o take_v this_o 1_o hour_n 1_o minute_n the_o ascensional_a difference_n out_o of_o 6_o hour_n and_o there_o will_v rest_v 4_o hour_n 59_o minute_n for_o the_o semidiurnal_a arch_n which_o be_v double_v give_v 9_o hour_n 58_o minute_n for_o the_o length_n of_o the_o day_n the_o compliment_n unto_o 24_o hour_n be_v 14_o hour_n 2_o minute_n the_o length_n of_o the_o night_n the_o half_a of_o which_o be_v 7_o hour_n 1_o min._n the_o time_n of_o sunrising_n chap._n xix_o have_v the_o latitude_n of_o the_o place_n &_o the_o declination_n of_o the_o sun_n to_o find_v the_o time_n of_o the_o beginning_n or_o end_v of_o twilight_n the_o beginning_n of_o twilight_n be_v when_o the_o sun_n approach_v within_o 18_o degree_n of_o the_o horizon_n in_o the_o east_n and_o the_o end_n of_o the_o same_o at_o 18_o deg_fw-la depression_n in_o the_o west_n wherefore_o to_o find_v the_o same_o work_n thus_o first_o by_o the_o 16_o chap._n get_v the_o height_n of_o the_o sun_n at_o the_o hour_n of_o six_o if_o the_o declination_n be_v north_n but_o if_o it_o be_v south_n take_v his_o depression_n at_o six_o for_o all_o be_v one_o thing_n if_o his_o quantity_n of_o declination_n be_v alike_o the_o height_n or_o depression_n at_o six_o be_v know_v if_o the_o declination_n be_v north_n add_v the_o sine_fw-la of_o this_o height_n to_o the_o sine_fw-la of_o 18_o deg_fw-la but_o if_o the_o declination_n be_v south_n take_v the_o difference_n betwixt_o the_o sine_fw-la of_o his_o depression_n and_o the_o sine_fw-la of_o 18_o deg_fw-la so_o shall_v the_o sum_n of_o difference_n be_v the_o second_o proportional_a number_n then_o say_v as_o the_o cousin_n of_o the_o latitude_n to_o this_o second_o proportional_a so_o be_v the_o radius_fw-la to_o a_o four_o proportional_a sine_fw-la then_o as_o the_o cousin_n of_o the_o declination_n to_o this_o four_o sine_fw-la so_o be_v the_o radius_fw-la to_o the_o sine_fw-la of_o the_o quantity_n of_o time_n between_o the_o beginning_n or_o end_v of_o twilight_n and_o the_o hour_n of_o six_o thus_o in_o the_o diagram_n of_o the_o 6_o chap._n have_v the_o declination_n of_o the_o sun_n ♈_o o_fw-fr 11_o deg_fw-la 30_o min._n north_n and_o thereby_o the_o sun_n height_n at_o six_o ro_n 9_o deg_fw-la 6_o min._n we_o have_v give_v we_o in_o the_o triangle_n byo_n first_o the_o angle_n ybo_n the_o compliment_n of_o the_o latitude_n 37_o deg_fw-la 30_o min._n and_o then_o the_o side_n o_fw-fr y_fw-fr 467_o the_o radius_fw-la being_n 1000_o this_o side_n be_v make_v up_o of_o the_o sine_fw-la of_o the_o sun_n height_n at_o six_o 158_o and_o the_o sine_fw-la of_o 18_o deg_fw-la 309_o or_o by_o add_v of_o or_o 158_o to_o r_o y_fw-fr 309_o we_o have_v o_o y_fw-fr 467_o for_o the_o second_o proportional_a these_o be_v know_v with_o the_o right_a angle_n at_o you_o we_o may_v find_v the_o base_a bo_z by_o the_o 10_o chapter_n or_o 27_o chap._n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n upon_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 37_o deg_fw-la 30_o min._n with_o the_o right_a parallel_n of_o 467_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 90_o deg_fw-la at_o the_o right_n sine_fw-la of_o 50_o deg_fw-la 7_o min._n which_o be_v the_o base_a bo_o but_o see_v the_o radius_fw-la of_o this_o sine_z bo_z be_v but_o the_o cousin_n of_o the_o declination_n oh_o 78_o deg_fw-la 30_o min._n therefore_o i_o place_v the_o thread_n again_o at_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 78_o deg_fw-la 30_o min._n with_o the_o right_n sine_fw-la of_o this_o 50_o degr_n 7_o min._n and_o it_o will_v cut_v the_o contrary_a sine_fw-la of_o 90_o deg_fw-la at_o the_o right_n sine_fw-la of_o 51_o deg_fw-la 33_o min._n and_o such_o be_v the_o distance_n of_o time_n between_o the_o hour_n of_o six_o and_o the_o beginning_n or_o end_v of_o twilight_n be_v 3_o hour_n 26_o min._n now_o at_o all_o time_n if_o you_o take_v this_o distance_n out_o of_o six_o hour_n your_o remainder_n shall_v be_v the_o beginning_n of_o twilight_n and_o if_o you_o add_v this_o distance_n find_v unto_o 6_o hour_n the_o sum_n will_v be_v the_o end_n of_o the_o same_o except_o it_o be_v in_o those_o latitude_n where_o the_o depression_n of_o 6_o be_v great_a than_o 18_o deg_fw-la and_o then_o you_o must_v in_o that_o latitude_n and_o south_n declination_n who_o depression_n at_o six_o be_v more_o than_o 18_o deg_fw-la work_n by_o the_o contrary_a rule_n and_o when_o the_o sun_n have_v north_n declination_n if_o you_o take_v the_o ascensional_a difference_n out_o of_o the_o distance_n of_o time_n between_o the_o hour_n of_o six_o and_o the_o beginning_n or_o end_v of_o twilight_n you_o shall_v have_v the_o distance_n of_o time_n between_o snn_n rise_v or_o set_v and_o the_o beginning_n or_o end_v of_o twilight_n and_o when_o the_o declination_n be_v south_n add_v the_o ascensional_a difference_n to_o the_o distance_n of_o time_n find_v and_o you_o shall_v have_v the_o quantity_n of_o twilight_n as_o before_o as_o for_o example_n let_v the_o distance_n of_o time_n between_o the_o beginning_n or_o end_v of_o twilight_n and_o the_o hour_n of_o six_o be_v find_v to_o be_v 3_o hour_n 26_o min._n if_o i_o take_v this_o 3_o hour_n 26_o min._n out_o of_o 6_o hour_n there_o will_v remain_v 2_o hour_n 34_o min_fw-mi for_o the_o beginning_n of_o twilight_n and_o if_o i_o add_v this_o 3_o hour_n 26_o min._n to_o six_o hour_n it_o will_v make_v 9_o hour_n 26_o min._n for_o the_o end_n of_o twilight_n and_o now_o be_v the_o sun_n have_v north_n declination_n if_o i_o take_v the_o difference_n of_o ascension_n 1_o hour_n 1_o min._n as_o it_o be_v find_v by_o the_o last_o chapter_n out_o of_o 3_o hour_n 26_o min._n there_o will_v remain_v 2_o hour_n 25_o min._n for_o the_o quantity_n of_o twilight_n before_o or_o after_o sun_n rise_v or_o set_v chap._n xx._n have_v the_o distance_n of_o the_o sun_n from_o the_o next_o equinoctial_a point_n to_o find_v his_o right_a ascension_n as_o the_o radius_fw-la to_o the_o cousin_n of_o the_o great_a declination_n so_o be_v the_o tangent_fw-la of_o the_o distance_n to_o the_o tangent_fw-la of_o the_o right_a ascension_n thus_o in_o the_o right_a angle_a triangle_n ♈_o x_o ♉_o in_o the_o diagram_n of_o the_o 6_o chap._n have_v the_o angle_n x_o ♈_o ♉_o the_o sun_n great_a declination_n 23_o deg_fw-la 30_o min._n and_o the_o base_a ♈_o ♉_o the_o distance_n of_o the_o sun_n from_o the_o equinoctial_a point_n ♈_o 30_o deg_fw-la with_o the_o right_a angle_n at_o x_o we_o may_v find_v the_o side_n ♈_o x_o the_o sun_n right_a ascension_n by_o the_o 33_o chap._n of_o the_o second_o book_n for_o if_o we_o place_v the_o thread_n at_o the_o intersection_n of_o the_o contrary_a sine_fw-la of_o 90_o deg_fw-la with_o the_o right_n tangent_fw-la of_o 30_o deg_fw-la it_o will_v cut_v the_o contrary_a sine_fw-la of_o 66_o degree_n 30_o minute_n at_o the_o right_n tangent_fw-la of_o 27_o degree_n 54_o minute_n and_o so_o much_o be_v the_o side_n ♈_o x_o the_o right_a ascension_n require_v chap._n xxi_o have_v the_o right_a ascension_n of_o the_o sun_n or_o star_n together_o with_o the_o difference_n of_o their_o ascension_n to_o find_v the_o oblique_a ascension_n and_o descension_n if_o the_o declination_n of_o the_o sun_n or_o star_n be_v north_n subtract_v the_o ascensional_a difference_n from_o the_o right_a ascension_n and_o the_o residue_n will_v be_v the_o oblique_a ascension_n but_o if_o you_o add_v they_o together_o the_o sum_n will_v be_v the_o oblique_a descension_n but_o if_o the_o declination_n be_v south_n add_v the_o ascensional_a difference_n and_o right_a ascension_n together_o so_o will_v the_o sum_n thereof_o be_v the_o oblique_a ascension_n but_o if_o you_o take_v the_o ascensional_a difference_n out_o of_o the_o right_a ascension_n the_o remainder_n will_v be_v the_o oblique_a descension_n as_o for_o example_n the_o right_a ascension_n of_o the_o sun_n in_o the_o begin_n of_o ♉_o being_z find_v by_o the_o last_o chapter_n to_o be_v 27_o degree_n 54_o minute_n and_o the_o ascensional_a

the_o almicanter_n the_o thread_n be_v thus_o place_v upon_o the_o 11_o deg_fw-la 30_o min._n in_o the_o axletree-line_n and_o parallel_v to_o the_o horizon_n will_v cut_v at_o each_o end_n thereof_o 9_o deg_fw-la 6_o min._n among_o the_o almicanter_n and_o such_o be_v the_o height_n of_o the_o sun_n at_o the_o hour_n of_o six_o or_o if_o you_o place_v the_o equator_fw-la 52_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o horizon_n and_o then_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o horizon_n where_o you_o shall_v find_v meet_v you_o a_o parallel_n which_o be_v follow_v to_o the_o axletree-line_n shall_v there_o give_v you_o 9_o deg_fw-la 6_o min._n for_o the_o altitude_n of_o the_o sun_n at_o six_o as_o before_o chap._n xxxvi_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v his_o azimuth_n at_o the_o hour_n of_o six_o first_o set_v the_o sphere_n according_a to_o the_o latitude_n give_v and_o count_v the_o declination_n upon_o the_o horizon_n and_o look_v what_o parallel_n there_o meet_v you_o the_o same_o follow_v to_o the_o axtree-line_n where_o it_o will_v show_v you_o the_o azimuth_n desire_v as_o in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n first_o i_o place_v the_o equator_fw-la at_o 37_o deg_fw-la 30_o min._n above_o the_o south_n end_n of_o the_o horizon_n and_o count_v the_o declination_n 11_o deg_fw-la 30_o min_fw-mi upon_o the_o horizon_n where_o i_o find_v to_o meet_v i_o the_o parallel_n of_o 7_o deg_fw-la 4_o min._n and_o such_o be_v the_o azimuth_n from_o the_o east_n or_o west_n point_v northwards_o chap._n xxxvii_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v the_o ascensional_a difference_n and_o consequent_o the_o time_n of_o sunrising_n and_o set_v with_o the_o diurnal_a and_o nocturnal_a arch_n first_o set_v the_o planisphere_n to_o the_o latitude_n give_v and_o reckon_v the_o declination_n upon_o the_o axletree-line_n follow_v low_o the_o parallel_n thereof_o to_o the_o horizon_n where_o you_o shall_v find_v meet_v you_o the_o meridian_n of_o the_o ascensional_a difference_n count_v from_o the_o hour_n of_o six_o and_o this_o same_o meridian_n give_v you_o the_o time_n of_o sun_n set_v count_v from_o the_o south_n part_n of_o the_o limb_n or_o general_a meridian_n and_o likewise_o the_o time_n of_o his_o rise_n count_v from_o the_o north_n part_n of_o the_o limb_n and_o now_o if_o you_o still_o note_v this_o intersection_n of_o the_o horizon_n and_o sun_n parallel_n and_o count_v the_o hour_n thereupon_o between_o the_o south_n part_n of_o the_o limb_n and_o the_o horizon_n you_o shall_v have_v the_o sun_n semidiurnal_a arch_n and_o from_o the_o horizon_n to_o the_o north_n part_n of_o the_o limb_n his_o seminocturnal_a arch_n both_o which_o be_v double_v give_v you_o both_o the_o diurnal_a and_o nocturnal_a arch_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o degree_n 30_o minute_n and_o the_o declination_n 11_o degree_n 30_o minute_n first_o i_o set_v the_o equator_fw-la 37_o degree_n 30_o minute_n above_o the_o horizon_n then_o count_v 11_o degree_n 30_o minute_n upon_o the_o axtree-line_n i_o follow_v the_o parallel_n thereof_o to_o the_o horizon_n where_o i_o find_v meet_v i_o the_o meridian_n of_o 15_o deg_fw-la 22_o min._n and_o such_o be_v the_o difference_n of_o ascensionals_n require_v now_o upon_o the_o same_o parallel_n of_o declination_n i_o seek_v how_o many_o hour_n i_o can_v find_v betweeene_v the_o south_n part_n of_o the_o limb_n and_o the_o horizon_n which_o be_v 7_o hour_n 1_o minute_n and_o so_o much_o be_v the_o semidiurnal_a arch_n and_o the_o time_n of_o sun_n set_v which_o be_v double_v make_v 14_o hour_n 2_o minute_n the_o diurnal_a arch_n so_o likewise_o count_v the_o hour_n between_o the_o north_n part_n of_o the_o limb_n and_o the_o horizon_n i_o find_v they_o 4_o hour_n 59_o minute_n and_o such_o be_v the_o seminocturnal_a arch_n and_o the_o time_n of_o sunrising_n which_o be_v double_v give_v 9_o hour_n 58_o min._n for_o the_o nocturnal_a arch_n the_o semidiurual_a and_o seminocturnal_a arch_n of_o any_o star_n who_o declination_n be_v know_v may_v be_v find_v in_o the_o self_n same_o manner_n chap._n xxxviii_o have_v the_o latitude_n of_o the_o place_n and_o the_o declination_n of_o the_o sun_n to_o find_v the_o time_n of_o the_o beginning_n and_o end_v of_o twilight_n first_o set_v the_o sphere_n to_o the_o latitude_n give_v then_o count_v the_o declination_n upon_o the_o axtree-line_n either_o northward_o or_o southward_o according_a as_o it_o be_v and_o then_o place_v the_o thread_n parallel_n to_o the_o horizon_n to_o the_o 18_o deg_fw-la of_o depression_n below_o the_o same_o and_o note_v where_o it_o cut_v the_o parallel_n of_o declination_n for_o those_o hour_n to_o the_o southward_n of_o the_o thread_n give_v the_o time_n of_o twilight_n end_v and_o the_o other_o to_o the_o northward_o the_o time_n of_o its_o beginning_n as_o for_o example_n let_v the_o latitude_n give_v be_v 52_o degree_n 30_o minute_n and_o the_o declination_n of_o the_o sun_n 11_o deg_fw-la 30_o min._n first_o i_o set_v the_o equator_fw-la 37_o deg_fw-la 30_o min._n above_o the_o horizon_n and_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o axletree-line_n northward_o because_o his_o declination_n be_v towards_o that_o pole_n i_o place_v the_o thread_n parallel_v to_o the_o horizon_n 18_o deg_fw-la below_o the_o same_o and_o i_o find_v it_o cut_v the_o say_a parallel_n of_o 11_o deg_fw-la 30_o min._n at_o 2_o hour_n 34_o minute_n from_o the_o north_n part_n of_o the_o limb_n and_o such_o be_v the_o time_n of_o the_o begin_n of_o twilight_n so_o do_v it_o likewise_o cut_v the_o same_o parallel_n at_o 9_o hour_n 26_o minute_n from_o the_o south_n part_n of_o the_o meridian_n and_o such_o be_v the_o time_n of_o the_o end_n of_o twilight_n which_o be_v require_v chap._n thirty-nine_o the_o latitude_n of_o the_o place_n the_o altitude_n and_o declination_n of_o the_o sun_n be_v give_v to_o find_v the_o hour_n of_o the_o day_n first_o place_v the_o planisphere_n to_o the_o latitude_n give_v and_o seek_v his_o declination_n on_o the_o axletree-line_n among_o the_o parallel_n of_o declination_n then_o place_v the_o thread_n parallel_n to_o the_o horizon_n to_o the_o degree_n of_o the_o sun_n altitude_n count_v from_o the_o horizon_n among_o the_o almicanter_n and_o where_o the_o thread_n so_o place_v shall_v cut_v the_o parallel_n of_o declination_n there_o pass_v by_o the_o meridian_n which_o give_v you_o the_o hour_n of_o the_o day_n as_o for_o example_n in_o the_o latitude_n of_o 52_o deg_fw-la 30_o min._n the_o declination_n of_o the_o sun_n be_v 11_o deg_fw-la 30_o min._n and_o his_o altitude_n 25_o deg_fw-la 56_o min._n i_o set_v the_o equator_fw-la 37_o deg_fw-la 30_o min._n above_o the_o horizon_n and_o count_v 11_o deg_fw-la 30_o min._n upon_o the_o axletree-line_n then_o place_v the_o thread_n to_o 25_o deg_fw-la 56_o min._n among_o the_o almicanter_n i_o find_v it_o cut_v the_o parallel_n of_o 11_o deg_fw-la 30_o min._n at_o four_o hour_n 8_o minute_n from_o the_o meridian_n and_o so_o much_o be_v the_o hour_n of_o the_o day_n if_o the_o observation_n be_v make_v in_o the_o afternoon_n but_o if_o the_o observation_n be_v make_v before_o noon_n than_o be_v it_o 7_o a_o clock_n and_o 52_o min._n in_o the_o forenoon_n again_o let_v the_o latitude_n and_o declination_n be_v the_o same_o as_o before_z and_o the_o altitude_n give_v 42_o deg_fw-la 26_o min._n now_o if_o i_o place_v the_o thread_n to_o 42_o deg_fw-la 26_o min._n among_o the_o almicanter_n it_o will_v cut_v the_o parallel_n of_o 11_o deg_fw-la 30_o min._n at_o just_a two_o hour_n from_o the_o meridian_n so_o shall_v it_o be_v either_o ten_o a_o clock_n in_o the_o morning_n or_o two_o afternoon_n according_a to_o the_o observation_n chap._n xl._n the_o latitude_n of_o the_o place_n the_o sun_n altitude_n and_o declination_n be_v give_v to_o find_v his_o azimuth_n first_o set_v the_o sphere_n to_o the_o latitude_n give_v and_o then_o count_v your_o altitude_n among_o the_o parallel_n of_o declination_n and_o your_o declination_n among_o the_o almicanter_n so_o shall_v your_o meridian_n become_v azimuth_n and_o the_o work_n will_v be_v the_o same_o as_o in_o the_o former_a chapter_n only_o here_o by_o the_o way_n i_o will_v have_v you_o note_v that_o as_o your_o parallel_n and_o almicanter_n change_v office_n so_o must_v your_o north_n and_o south_n part_n of_o the_o general_a meridian_n change_v name_n so_o that_o when_o your_o thread_n cut_v any_o parallel_n at_o any_o azimuth_n if_o you_o count_v that_o azimuth_n from_o the_o south_n part_n of_o the_o limb_n it_o shall_v